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Spaceplates are novel flat-optic devices that implement the optical response of a free-space volume over a smaller length, effectively “compressing space” for light propagation. Together with flat lenses such as metalenses or diffractive lenses, spaceplates have the potential to enable the miniaturization of any free-space optical system. While the fundamental and practical bounds on the performance metrics of flat lenses have been well studied in recent years, a similar understanding of the ultimate limits of spaceplates is lacking, especially regarding the issue of bandwidth, which remains as a crucial roadblock for the adoption of this platform. In this work, we derive fundamental bounds on the bandwidth of spaceplates as a function of their numerical aperture and compression ratio (ratio by which the free-space pathway is compressed). The general form of these bounds is universal and can be applied and specialized for different broad classes of space-compression devices, regardless of their particular implementation. Our findings also offer relevant insights into the physical mechanism at the origin of generic space-compression effects and may guide the design of higher performance spaceplates, opening new opportunities for ultra-compact, monolithic, planar optical systems for a variety of applications.

Limited-size receiver (Rx) apertures and transmitter–Rx (Tx–Rx) misalignments could induce power loss and modal crosstalk in a mode-multiplexed free-space link. We experimentally demonstrate the mitigation of these impairments in a 400 Gbit/s four-data-channel free-space optical link. To mitigate the above degradations, our approach of singular-value-decomposition-based (SVD-based) beam orthogonalization includes (1) measuring the transmission matrix$\text{H}$for the link given a limited-size aperture or misalignment; (2) performing SVD on the transmission matrix to find the$\text{U}$,$\mathrm{\Sigma <\#comment/>}$, and$\text{V}$complex matrices; (3) transmitting each data channel on a beam that is a combination of Laguerre–Gaussian modes with complex weights according to the$\text{V}$matrix; and (4) applying the$\text{U}$matrix to the channel demultiplexer at the Rx. Compared with the case of transmitting each channel on a beam using a single mode, our experimental results when transmitting multi-mode beams show that (a) with a limited-size aperture, the power loss and crosstalk could be reduced by$\sim <\#comment/>8$and$\sim <\#comment/>23\text{dB}$, respectively; and (b) with misalignment, the power loss and crosstalk could be reduced by$\sim <\#comment/>15$and$\sim <\#comment/>40\text{dB}$, respectively.

We experimentally demonstrate the utilization of adaptive optics (AO) to mitigate intra-group power coupling among linearly polarized (LP) modes in a graded-index few-mode fiber (GI FMF). Generally, in this fiber, the coupling between degenerate modes inside a modal group tends to be stronger than between modes belonging to different groups. In our approach, the coupling inside the${\mathrm{L}\mathrm{P}}_{11}$group can be represented by a combination of orbital-angular-momentum (OAM) modes, such that reducing power coupling in OAM set tends to indicate the capability to reduce the coupling inside the${\mathrm{L}\mathrm{P}}_{11}$group. We employ two output OAM modes$l=+1$and$l=-<\#comment/>1$as resultant linear combinations of degenerate${\mathrm{L}\mathrm{P}}_{11\mathrm{a}}$and${\mathrm{L}\mathrm{P}}_{11\mathrm{b}}$modes inside the${\mathrm{L}\mathrm{P}}_{11}$group of a$\sim <\#comment/>0.6\text{-}\mathrm{k}\mathrm{m}$GI FMF. The power coupling is mitigated by shaping the amplitude and phase of the distorted OAM modes. Each OAM mode carries an independent 20-, 40-, or 100-Gbit/s quadrature-phase-shift-keying data stream. We measure the transmission matrix (TM) in the OAM basis within${\mathrm{L}\mathrm{P}}_{11}$group, which is a subset of the full LP TMmore »of the FMF-based system. An inverse TM is subsequently implemented before the receiver by a spatial light modulator to mitigate the intra-modal-group power coupling. With AO mitigation, the experimental results for$l=+1$and$l=-<\#comment/>1$modes show, respectively, that (i) intra-modal-group crosstalk is reduced by$><\#comment/>5.8\mathrm{d}\mathrm{B}$and$><\#comment/>5.6\mathrm{d}\mathrm{B}$and (ii) near-error-free bit-error-rate performance is achieved with a penalty of$\sim <\#comment/>0.6\mathrm{d}\mathrm{B}$and$\sim <\#comment/>3.8\mathrm{d}\mathrm{B}$, respectively.

We experimentally demonstrate simultaneous turbulence mitigation and channel demultiplexing in a 200 Gbit/s orbital-angular-momentum (OAM) multiplexed link by adaptive wavefront shaping and diffusing (WSD) the light beams. Different realizations of two emulated turbulence strengths (the Fried parameter$r_0=0.4,1.0\mathrm{m}\mathrm{m}$) are mitigated. The experimental results show the following. (1) Crosstalk between OAM$l=+1$and$l=-<\#comment/>1$modes can be reduced by$><\#comment/>10.0$and$><\#comment/>5.8\mathrm{d}\mathrm{B}$, respectively, under the weaker turbulence ($r_0=1.0\mathrm{m}\mathrm{m}$); crosstalk is further improved by$><\#comment/>17.7$and$><\#comment/>19.4\mathrm{d}\mathrm{B}$, respectively, under most realizations in the stronger turbulence ($r_0=0.4\mathrm{m}\mathrm{m}$). (2) The optical signal-to-noise ratio penalties for the bit error rate performance are measured to be$\sim <\#comment/>0.7$and$\sim <\#comment/>1.6\mathrm{d}\mathrm{B}$under weaker turbulence, while measured to be$\sim <\#comment/>3.2$and$\sim <\#comment/>1.8\mathrm{d}\mathrm{B}$under stronger turbulence for OAM$l=+1$and$l=-<\#comment/>1$mode, respectively.